DIVERSIFYING OUR PERSPECTIVES ON MATHEMATICS ABOUT SPACE AND GEOMETRY: AN ECOCULTURAL APPROACH

School mathematics tends to have developed from the major cultures of Asia, the Mediterranean and Europe. However, indigenous cultures in particular may have distinctly different systematic ways of referring to space and thinking mathematically about spatial activity. Their approaches are based on the close link between the environment and cultural activity. The affinity to place strengthens the efficient, abstract, mathematical system behind the reference and its connection to the real world of place and a holistic worldview. This paper sets out to present an overview of various approaches to aspects of space and geometry by drawing on linguistic and cultural literature, my collaborative research in Papua New Guinea, and from personal communications with indigenous colleagues in Australia and elsewhere. This diversity provides a challenge by which teachers can deconstruct their thinking about mathematics and subsequently to review the content of teaching and to be more responsive to the diversity of cultural backgrounds of students. To assist with recognising ecocultural mathematics on space and geometry, 4 principles are established and discussed on language structures, reference lines and points, measures of space and worldviews and interpretations of space as place.     

Physiological Profiles of High School Female Cross Country Runners

Abstract

Percent body fat, ratings of perceived exertion and maximal oxygen consumption during a continuous running treadmill test were obtained on 127 high school female cross country runners. These young runners (x 15.6 yrs) were running approximately 25 miles per week at the time of testing. They had an average [Vdot]O₂ max of 50.8 ml · min^-1 and an HR max of 198.0 bpm. The mean percent body fat, as determined from hydrostatic weighing, was 15.4%. The onset of metabolic acidosis was estimated to occur at 78% of [Vdot]O₂ max. A stepwise multiple regression with the 3000 meter run as the dependent variable indicated that max treadmill run time, weight relative [Vdot]O₂ max and [Vdot] max entered the equation in that order, yielding an R of 0.67. Both HR and RPE increased with work intensity, but not at equal rates. These high school female runners had higher [Vdot]O₂ max's than previously reported for this age group; however, they were considerably below these values reported for national caliber distance runners.     

Leadership in online learning in higher education: Why instructional designers for online learning should lead the way

With the increase in demand for online education at the university level has also come the “recognition that in order to be effective, such programs cannot simply be on‐line replicas of the instruction delivered in classrooms” (Reiser, 2001, p. 64). An environment of collaboration with a shared vision is needed to bring faculty expertise together with online learning design and technological expertise. This article addresses why and how instructional designers should lead the way.